Group #18019274 — subgroups

Subgroups — C₁₉×#13315 #18019274

Order 4864.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#473	C₂	1	2	yes	maximal
3	C₂×C₁₉×#362	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2113	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#137	—	2	2	no	—
7	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×Q₃₂	—	2	2	no	—
10	C₂×C₁₉×Q₃₂	—	2	4	no	—
11	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
12	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#473	—	2	4	no	—
14	C₁₉×#473	—	2	4	no	—
15	C₂×C₁₉×#108	C₂²	1	2	yes	—
16	C₂×C₁₉×#101	—	2	2	no	—
17	C₁₉×#362	—	2	4	no	—
18	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
19	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	2	no	—
21	C₁₉×#137	—	2	8	no	—
22	C₁₉×#137	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	2	no	—
24	C₂×Q₁₆×C₁₉	—	2	2	no	—
25	C₂×Q₁₆×C₁₉	—	2	2	no	—
26	C₂×Q₁₆×C₁₉	—	2	2	no	—
27	C₂×Q₁₆×C₁₉	—	2	2	no	—
28	C₂×Q₁₆×C₁₉	—	4	2	no	—
29	C₂×Q₁₆×C₁₉	D₄	1	4	yes	—
30	C₂×SD₁₆×C₁₉	—	4	2	no	—
31	C₁₉×#131	—	2	2	no	—
32	C₁₉×#131	—	2	2	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×Q₃₂	—	2	8	no	—
39	C₁₉×M₃₂	—	2	2	no	—
40	C₂×C₁₆×C₁₉	—	2	2	no	—
41	C₂×C₁₆×C₁₉	—	2	1	no	—
42	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
43	C₁₉×#108	—	2	2	no	—
44	C₁₉×#108	D₄	1	4	yes	—
45	C₁₉×#101	—	2	8	no	—
46	#41×C₁₉	—	2	2	no	—
47	#41×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	4	no	—
49	C₂×Q₈×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
55	C₂×D₄×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	Q₁₆×C₁₉	—	2	4	no	—
61	Q₁₆×C₁₉	—	2	4	no	—
62	Q₁₆×C₁₉	—	4	8	no	—
63	Q₁₆×C₁₉	—	4	2	no	—
64	Q₁₆×C₁₉	—	4	2	no	—
65	SD₁₆×C₁₉	—	4	8	no	—
66	M₁₆×C₁₉	—	2	4	no	—
67	M₁₆×C₁₉	—	2	2	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	M₁₆×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	2	1	no	—
71	C₂×C₈×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	4	1	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
78	C₁₆×C₁₉	—	2	2	no	—
79	C₁₆×C₁₉	—	4	1	no	—
80	#13315	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂³×C₁₉	—	2	1	no	—
82	C₂³×C₁₉	#135	1	1	yes	characteristic
83	Q₈×C₁₉	—	2	2	no	—
84	Q₈×C₁₉	—	4	4	no	—
85	Q₈×C₁₉	—	4	4	no	—
86	Q₈×C₁₉	—	8	2	no	—
87	Q₈×C₁₉	—	8	2	no	—
88	D₄×C₁₉	—	2	2	no	—
89	D₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	4	no	—
94	C₂×C₄×C₁₉	—	8	2	no	—
95	C₂×C₄×C₁₉	—	8	2	no	—
96	C₂×C₄×C₁₉	#120	1	2	yes	—
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₈×C₁₉	—	4	1	no	—
101	C₈×C₁₉	—	4	4	no	—
102	C₈×C₁₉	#120	1	1	yes	characteristic
103	C₈×C₁₉	#121	1	2	yes	—
104	C₈×C₁₉	#127	1	1	yes	characteristic
105	C₂²×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
106	C₂×#473	C₂×C₁₉	1	2	yes	—
107	C₂×#362	C₂×C₁₉	1	2	yes	complemented
108	#2113	C₂×C₁₉	1	1	yes	characteristic
109	#1381	C₂×C₁₉	1	1	yes	characteristic, complemented
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	4	2	no	—
112	C₂²×C₁₉	—	4	1	no	—
113	C₂²×C₁₉	#449	1	2	yes	—
114	C₂²×C₁₉	#466	1	1	yes	characteristic
115	C₄×C₁₉	—	4	1	no	—
116	C₄×C₁₉	—	8	4	no	—
117	C₄×C₁₉	#392	1	1	yes	characteristic
118	C₄×C₁₉	#447	1	2	yes	—
119	C₄×C₁₉	#469	1	1	yes	characteristic
120	C₂×#137	—	2	2	no	—
121	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
122	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
123	C₂×Q₃₂	—	2	4	no	—
124	C₂×Q₃₂	—	2	2	no	—
125	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
126	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
127	#473	—	2	4	no	—
128	#473	—	2	4	no	—
129	C₂×#108	C₂²×C₁₉	1	2	yes	—
130	C₂×#101	—	2	2	no	—
131	#362	—	2	4	no	—
132	C₂²⋊C₁₆	—	2	2	no	—
133	C₂×C₁₉	—	2	2	no	—
134	C₂×C₁₉	—	8	1	no	—
135	C₂×C₁₉	#1999	1	1	yes	characteristic
136	C₂×C₁₉	#2222	1	2	yes	—
137	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
138	C₂²×Q₈	—	2	2	no	—
139	#137	—	2	8	no	—
140	#137	—	4	4	no	—
141	C₂×Q₁₆	—	2	2	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	—	2	2	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	—	4	2	no	—
147	C₂×Q₁₆	D₄×C₁₉	1	4	yes	—
148	C₂×SD₁₆	—	4	2	no	—
149	#131	—	2	2	no	—
150	#131	—	2	2	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
156	Q₃₂	—	2	8	no	—
157	M₃₂	—	2	2	no	—
158	C₂×C₁₆	—	2	2	no	—
159	C₂×C₁₆	—	2	1	no	—
160	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
161	#108	—	2	2	no	—
162	#108	D₄×C₁₉	1	4	yes	—
163	#101	—	2	8	no	—
164	C₁₉	#13315	1	1	yes	characteristic, direct product factor, Sylow
165	#41	—	2	2	no	—
166	#41	—	2	2	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	2	no	—
173	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
179	Q₁₆	—	2	4	no	—
180	Q₁₆	—	2	4	no	—
181	Q₁₆	—	4	8	no	—
182	Q₁₆	—	4	2	no	—
183	Q₁₆	—	4	2	no	—
184	SD₁₆	—	4	8	no	—
185	M₁₆	—	2	2	no	—
186	M₁₆	—	2	4	no	—
187	M₁₆	—	4	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
194	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
195	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
196	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
197	C₁₆	—	2	2	no	—
198	C₁₆	—	4	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	C₁₉×#135	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	4	4	no	—
203	Q₈	—	4	4	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	8	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	4	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	—	8	2	no	—
214	C₂×C₄	C₁₉×#120	1	2	yes	—
215	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
216	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
217	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
218	C₈	—	4	1	no	—
219	C₈	—	4	4	no	—
220	C₈	C₁₉×#120	1	1	yes	characteristic
221	C₈	C₁₉×#121	1	2	yes	—
222	C₈	C₁₉×#127	1	1	yes	characteristic
223	C₂²	—	2	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	1	no	—
226	C₂²	C₁₉×#449	1	2	yes	—
227	C₂²	C₁₉×#466	1	1	yes	characteristic
228	C₄	—	4	1	no	—
229	C₄	—	8	4	no	—
230	C₄	C₁₉×#392	1	1	yes	characteristic
231	C₄	C₁₉×#447	1	2	yes	—
232	C₄	C₁₉×#469	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	—	8	1	no	—
235	C₂	C₁₉×#1999	1	1	yes	characteristic
236	C₂	C₁₉×#2222	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#473

C₂

yes

maximal

C₂×C₁₉×#362

C₂

yes

maximal, complemented

C₁₉×#2113

C₂

yes

maximal, characteristic

C₁₉×#1381

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#137

—

C₂²×Q₁₆×C₁₉

C₂²

yes

—

C₂×C₁₉×#131

C₂²

yes

characteristic

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#473

—

C₁₉×#473

—

C₂×C₁₉×#108

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#362

—

C₁₉×C₂²⋊C₁₆

—

C₂×#41×C₁₉

D₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂×SD₁₆×C₁₉

—

C₁₉×#131

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

—

C₁₉×#108

—

C₁₉×#108

D₄

yes

—

C₁₉×#101

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

#41

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#13315

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#135

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

#120

yes

characteristic

103

C₈×C₁₉

#121

yes

—

104

C₈×C₁₉

#127

yes

characteristic

105

C₂²×Q₃₂

C₂×C₁₉

yes

characteristic, complemented

106

C₂×#473

C₂×C₁₉

yes

—

107

C₂×#362

C₂×C₁₉

yes

complemented

108

#2113

C₂×C₁₉

yes

characteristic

109

#1381

C₂×C₁₉

yes

characteristic, complemented

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#449

yes

—

114

C₂²×C₁₉

#466

yes

characteristic

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#392

yes

characteristic

118

C₄×C₁₉

#447

yes

—

119

C₄×C₁₉

#469

yes

characteristic

120

C₂×#137

—

121

C₂²×Q₁₆

C₂²×C₁₉

yes

—

122

C₂×#131

C₂²×C₁₉

yes

characteristic

123

C₂×Q₃₂

—

124

C₂×Q₃₂

—

125

C₂×M₃₂

C₂²×C₁₉

yes

characteristic

126

C₂²×C₁₆

C₂²×C₁₉

yes

characteristic

127

#473

—

128

#473

—

129

C₂×#108

C₂²×C₁₉

yes

—

130

C₂×#101

—

131

#362

—

132

C₂²⋊C₁₆

—

133

C₂×C₁₉

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1999

yes

characteristic

136

C₂×C₁₉

#2222

yes

—

137

C₂×#41

D₄×C₁₉

yes

characteristic

138

C₂²×Q₈

—

139

#137

—

140

#137

—

141

C₂×Q₁₆

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

D₄×C₁₉

yes

—

148

C₂×SD₁₆

—

149

#131

—

150

#131

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

D₄×C₁₉

yes

characteristic

154

C₂²×C₈

—

155

C₂²×C₈

C₂³×C₁₉

yes

characteristic

156

Q₃₂

—

157

M₃₂

—

158

C₂×C₁₆

—

159

C₂×C₁₆

—

160

C₂×C₁₆

D₄×C₁₉

yes

—

161

#108

—

162

#108

D₄×C₁₉

yes

—

163

#101

—

164

C₁₉

#13315

yes

characteristic, direct product factor, Sylow

165

#41

—

166

#41

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

D₈×C₁₉

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

D₈×C₁₉

yes

characteristic

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

179

Q₁₆

—

180

Q₁₆

—

181

Q₁₆

—

182

Q₁₆

—

183

Q₁₆

—

184

SD₁₆

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

C₂×D₄×C₁₉

yes

—

194

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

195

C₂×C₈

C₂×D₄×C₁₉

yes

—

196

C₂×C₈

#41×C₁₉

yes

characteristic

197

C₁₆

—

198

C₁₆

—

199

C₂³

—

200

C₂³

C₁₉×#135

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

C₁₉×#120

yes

—

215

C₂×C₄

C₁₉×#121

yes

characteristic

216

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

217

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

—

218

C₈

—

219

C₈

—

220

C₈

C₁₉×#120

yes

characteristic

221

C₈

C₁₉×#121

yes

—

222

C₈

C₁₉×#127

yes

characteristic

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

C₁₉×#449

yes

—

227

C₂²

C₁₉×#466

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

C₁₉×#392

yes

characteristic

231

C₄

C₁₉×#447

yes

—

232

C₄

C₁₉×#469

yes

characteristic

233

C₂

—

234

C₂

—

235

C₂

C₁₉×#1999

yes

characteristic

236

C₂

C₁₉×#2222

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#466

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₂×#41×C₁₉

D₄

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

N	H ≅ G/N	type
1. C₂²×C₁₉×Q₃₂	C₂	semidirect
3. C₂×C₁₉×#362	C₂	semidirect
5. C₁₉×#1381	C₂	semidirect
80. #13315	C₁₉	direct (N × H)
105. C₂²×Q₃₂	C₂×C₁₉	semidirect
107. C₂×#362	C₂×C₁₉	semidirect
109. #1381	C₂×C₁₉	semidirect
164. C₁₉	#13315	direct (N × H)

H ≅ G/N

type

1. C₂²×C₁₉×Q₃₂

C₂

semidirect

3. C₂×C₁₉×#362

C₂

semidirect

5. C₁₉×#1381

C₂

semidirect

80. #13315

C₁₉

direct (N × H)

105. C₂²×Q₃₂

C₂×C₁₉

semidirect

107. C₂×#362

C₂×C₁₉

semidirect

109. #1381

C₂×C₁₉

semidirect

164. C₁₉

#13315

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₉×Q₃₂	2
C₂×C₁₉×#473	2
C₂×C₁₉×#362	2
C₁₉×#2113	2
C₁₉×#1381	2
#13315	19

subgroup

index

C₂²×C₁₉×Q₃₂

C₂×C₁₉×#473

C₂×C₁₉×#362

C₁₉×#2113

C₁₉×#1381

#13315

Subgroups — C₁₉×#13315 #18019274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13315 #18019274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13315 #18019274